Power driven reamers or bone cutters are utilized to round out and reshape the cavity or socket of the hip, following the destruction of cartilage or bone at the hip socket. Such power driven bone cutters utilize a plurality of blades having the cutting edges projecting slightly from the rotary hemispherical head of the cutter. In U.S. Pat. No. 3,633,583 to Meyer Fishbein granted Jan. 11, 1972, there is shown a substantially hemispherical head in which a single surgical blade is so shaped as to provide two radially disposed cutting edges on opposite sides of the rotational center line of the head. The edges project just slightly above the adjustment substantially hemispherical surface of the cutting head and the cutting edges are beveled in opposite directions on opposide sides of the axis of rotation so that both edges will cut during rotation of the head. Troughs or grooves are formed in the head forward of the cutting edges to transport the cut material from the surface of the head to the back end of the head. Thus, loose cut material can be present at the site of the cutting operation. Further, in this prior device, the manner in which the cutter head is attached to the drive shaft does not make it possible to quickly change the cutter head. In some cutting operations, more than one size of hemispherical cutter head must be utilized to obtain the necessary change in dimension of the socket, particularly in the case where a plastic sleeve is to be added to the socket, and quick changing of the cutter heads is desirable in this case. Also, since the cutting edges of the prior device are 180.degree. apart, there is less resistance to tipping of the rotating axis of the cutter head than if more blades were utilized.